We present a study of the average transverse momentum (p[subscript t]) fluctuations and p[subscript t] correlations for charged particles produced in Cu+Cu collisions at midrapidity for √s[subscript NN]= 62.4 and 200 GeV. These results are compared with those published for Au+Au collisions at the same energies, to explore the system size dependence. In addition to the collision energy and system size dependence, the p[subscript t] correlation results have been studied as functions of the collision centralities, the ranges in p[subscript t], the pseudorapidity η, and the azimuthal angle ϕ. The square root of the measured p[subscript t] correlations when scaled by mean p[subscript t] is found to be independent of both colliding beam energy and system size studied. Transport-based model calculations are found to have a better quantitative agreement with the measurements compared to models which incorporate only jetlike correlations.